Many imaging systems, for example radiography systems such as X-ray imaging systems, produce an image of a subject by passing illuminating radiation through the subject and forming on the other side an image consisting of a map of the varying degrees of attenuation of the illuminating radiation. This is the basis of the traditional X-ray image used in medical and vetinerary practice, as well as in the analysis of inanimate objects, for example in security systems. However, there are a variety of factors which tend to degrade the image produced. On the illuminating side there may be non-uniformity in the illuminating radiation, e.g. the so-called “anode-heel effect” in X-ray imaging. Degradation may also occur in the detection of the transmitted radiation. For instance in the case of a film-screen system, film saturation, film grain noise, X-ray to light conversion noise and digitiser blur for films digitised using a scanner may be present. However, a significant source of degradation is scattering of the illuminating radiation in the imaged object. This is illustrated for a typical film-screen mammography apparatus in FIG. 1 of the accompanying drawings. As illustrated an X-ray tube 1 is used to illuminate a breast 3 held between top and bottom compression plates 5, 7 spaced a distance H apart. X-rays passing through the breast impinge on the phosphor screen 9 where their energy is converted to light which is recorded on the photographic film 11. The primary X-rays passing through the breast are illustrated by the solid arrows. However, some X-rays are scattered within the breast as indicated by the dotted arrows and thus impinge on other parts of the screen-film blurring the image. The same problem arises in digital systems where the film-screen is replaced by an electronic detector (for example consisting of a combination of a fluorescent screen with a matrix of sensors sensitive to light photons). In essence the scattering means that at every pixel on the resulting image, the intensity at that pixel is due not only to the primary X-ray, but also to scattered X-rays coming from elsewhere.
A traditional way to try to reduce the effect of scatter is to use an anti-scatter grid as illustrated in FIG. 2 of the accompanying drawings. This grid 13, typically formed of lead strips, blocks X-rays coming from oblique angles (i.e. scattered X-rays) but allows the primary X-rays coming directly from the X-ray source to pass through. In order that a complete image is obtained (without unexposed areas due to the presence of the grid), the grid is moved during the exposure. While such anti-scatter grids are effective, their presence reduces the intensity of the radiation incident on the detector and so it is necessary to increase the dosage of X-ray radiation. Often it is necessary to double the dosage and this is clearly undesirable.
An approach of calculating the amount of scatter from the image itself is described in the article “Computing the Scatter Component of Mammographic Images”, by Ralph Highnam, Michael Brady and Basil Shepstone published in IEEE Medical Image, 1994, 13, pp 301 to 313. This allows the calculation of the primary energy imparted to the detector by the subtraction of the energy due to scatter. With this approach the amount of energy reaching any pixel because of scattering is assumed to be related to, and is calculated from, the intensity of the radiation reaching the pixels in a surrounding neighbourhood. Thus the contribution due to scatter can be calculated by convoluting the intensities at the surrounding pixels with a “scatter mask”. Typically the scatter mask is a cylindrically symmetric function such as that illustrated in FIG. 3. It should be noted that the scatter mask is computed for the radiography system in question, and is adjusted depending on the compressed breast thickness H. Such a scatter mask can be defined for both systems using an anti-scatter grid and systems without.
Thus the primary energy Ep imparted to the detector at a pixel (xc,yc) isEp(xc,yc)=E(xc,yc)−Es(xc,yc)where Es(xc,yc) is the energy due to scatter and E(xc,yc) is the total energy imparted to the pixel (xc,yc). With this approach the energy due to scatter is calculated by convolving the energy values in a neighbourhood N around (xc,yc) with a scatter mask w and multiplying by a linear scatter function s:
            E      s        ⁡          (                        x          c                ,                  y          c                    )        =      s    ⁡          (                        ∑                                    (                                                                    x                    c                                    -                  x                                ,                                                      y                    c                                    -                  y                                            )                        ∈            N                                                          ⁢                              E            ⁡                          (                                                                    x                    c                                    -                  x                                ,                                                      y                    c                                    -                  y                                            )                                ⁢                      w            ⁡                          (                              x                ,                y                            )                                          )      
A more recent way of minimising scattered radiation without using an anti-scatter grid is to use a so-called slot-scanning system. In such a system, rather than the whole, full-field image being obtained simultaneously, a narrow collimated beam of radiation is used together with a correspondingly narrow detector. The beam and detector are scanned across the subject. This is illustrated schematically for a mammography system in FIGS. 4 and 5. As illustrated a conventional X-ray source 1 is used but the radiation is collimated into a narrow beam by a collimator 15 and a correspondingly narrow detector 17 is used. To scan the image the collimator 15 detector 17 and X-ray source 1, which are all fixed to an arm to maintain alignment, are rotated about the rotation axis 19.
The effect of using a narrow beam and narrow detector is that the amount of scatter reaching the detector is significantly reduced. In addition the detector may be mounted spaced below the bottom compression plate 7 by a distance A. This air gap reduces scatter in the narrow dimension direction of the detector, although it increases the amount of scatter recorded in the perpendicular direction. The air gap A also magnifies the image. It is also possible to adjust the collimator 15 so as to have a different width from the detector 17. This influences the amount of scatter received on the detector. Ideally the collimator should match the detector in size, but in practice it is slightly wider. A typical detector is made of several lines of sensors, about 200 in one example or 10 in another example, and the detector moves parallel to its narrow direction by a distance of one pixel for each exposure. Thus each pixel in the final image is created by the sum of responses of a line of sensors across the detector. This is known as “time delay integration”. FIG. 6 illustrates the principle in which a given pixel P at position 0 in the final image will receive signal for the whole time the detector overlaps position P, i.e. when the detector is in successive positions A B C D E and F as illustrated. For example, with a slot scanning system using a linear detector (e.g. in the SenoScan of 21 cm×1 cm) which is moving across the breast—the detector moves, an image is taken, it moves by one pixel, and another image is taken, etc. Thus the total exposure to a pixel in the image comes from several different exposures and not in just ‘one hit’. In fact in the detector a charge accumulation technique is used, so that the charge accumulated on one cell of the detector is transferred from cell to cell in the opposite direction to the motion of the detector as it moves so as to remain under the same image pixel. When it reaches the edge of the detector it is outputted as the total exposure for that image pixel.
Although the use of a slot scanning system is effective to reduce the amount of scatter in one direction, it does not eliminate scatter completely in that direction, and also gives no benefit in the perpendicular direction (the long direction of the detector). Further, as well as primary being accumulated at each pixel with the successive exposures, scatter is also accumulated. So the total exposure consists of the accumulated primary radiation and also the accumulated scatter. Even in such a slot scanning system, therefore, it would be useful to be able to reduce the degrading effect of scatter in the image. If the results of each individual exposure were known, a standard scatter function could be applied to each exposure to estimate scatter. However, in fact only the results of the accumulation of the exposures is obtained (the image), so the standard scatter mask cannot be applied.